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 A169677 The first of a pair of sequences A and B with property that all the differences |a_i - b_j| are distinct - for precise definition see Comments lines. 6
 0, 1, 7, 18, 35, 59, 88, 125, 178, 233, 285, 344, 352, 442, 557, 675, 796, 797, 957, 1011, 1220, 1411, 1564, 1579, 1888, 2120, 2152, 2503, 2829, 2953, 3393, 3464, 3593, 3724, 4237, 4956, 5310, 5388, 5968, 6478, 6756, 7344, 7698, 8004, 8182 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Consider pairs of sequences A = a_1 a_2 a_3 a_4 ... and B = b_1 b_2 b_3 ... such that 1: All the terms are nonnegative integers 2: The terms of A are strictly increasing 3: The terms of B are strictly increasing 4: All the numbers |a_i - b_j| are distinct 5: The terms are computed in the following order: a(1), b(1), a(2), b(2), ..., b(n-1), a(n), b(n), a(n+1), ... and always the smallest value is chosen that satisfies constraints 1-4. Computed by Alois P. Heinz and Wouter Meeussen, Mar 27 2010 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..200 MAPLE # Maple program from Alois P. Heinz: ab:=proc() false end: ab(0):=true: a:= proc(n) option remember; local ok, i, k, s; if n=1 then 0 else b(n-1); for k from a(n-1)+1 do ok:=true; for i from 1 to n-1 do if ab(abs(k-b(i))) then ok:= false; break fi od; if ok then s:={}; for i from 1 to n-1 do s:= s union {abs(k-b(i))}; od fi; if ok and nops(s)=n-1 then break fi od; for i from 1 to n-1 do ab(abs(k-b(i))):=true od; k fi end; b:= proc(n) option remember; local ok, i, k, s; if n=1 then 0 else a(n); for k from b(n-1)+1 do ok:=true; for i from 1 to n do if ab(abs(k-a(i))) then ok:= false; break fi od; if ok then s:={}; for i from 1 to n do s:= s union {abs(k-a(i))}; od fi; if ok and nops(s)=n then break fi od; for i from 1 to n do ab(abs(k-a(i))):=true od; k fi end; seq(a(n), n=1..80); seq(b(n), n=1..80); MATHEMATICA ClearAll[ab, a, b]; ab[_] = False; ab = True; a[n_] := a[n] = Module[{ ok, i, k, s}, If[ n == 1 , 0, b[n-1]; For[ k = a[n-1] + 1 , True, k++, ok = True; For[ i = 1 , i <= n-1, i++, If[ ab[Abs[k - b[i]]] , ok = False; Break[] ]]; If[ ok , s = {}; For[ i=1 , i <= n-1 , i++, s = s ~Union~ {Abs[k - b[i]]}; ]]; If[ ok && (Length[s] == n-1) , Break[] ]]; For[ i=1 , i <= n-1 , i++, ab[Abs[k - b[i]]] = True]; k]]; b[n_] := b[n] = Module[{ ok, i, k, s}, If[ n == 1 , 0, a[n]; For[ k = b[n-1] + 1 , True, k++, ok = True; For[ i=1 , i <= n, i++, If[ ab[Abs[k - a[i]]] , ok = False; Break[] ]]; If[ ok , s = {}; For[ i=1 , i <= n , i++, s = s ~Union~ {Abs[k - a[i]]}; ]]; If[ ok && Length[s] == n , Break[] ]]; For[ i=1 , i <= n, i++, ab[Abs[k - a[i]]] := True]; k]]; Table[a[n], {n, 1, 45}] (* Jean-François Alcover, Aug 13 2012, translated from Alois P. Heinz's Maple program *) CROSSREFS Cf. A169678, A169679, A169680, A169690-A169693. Sequence in context: A301709 A297646 A320281 * A263876 A192751 A272459 Adjacent sequences:  A169674 A169675 A169676 * A169678 A169679 A169680 KEYWORD nonn,nice AUTHOR R. K. Guy and N. J. A. Sloane, Mar 27 2010 EXTENSIONS Comments clarified by Zak Seidov and Alois P. Heinz, Apr 13 2010. STATUS approved

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Last modified April 8 23:02 EDT 2020. Contains 333331 sequences. (Running on oeis4.)